Forcing Chain

A candidate that forces a contradiction can be ruled out (Nishio).

Learn the Forcing Chain / Nishio technique: place a candidate and follow the forced singles; if they reach a contradiction, that candidate is impossible.

How to use it

  1. Pick a candidate to test. Choose a cell with two or more candidates and tentatively assume one of them is the answer for that cell.
  2. Follow the forced singles. Fill in every move that assumption forces — naked singles and hidden singles — one after another, as far as the chain runs.
  3. Rule it out on a contradiction. If the chain ever empties a cell of all candidates, or leaves a unit with no home for a digit, the assumption was wrong — remove that candidate from the starting cell.
Practice on a real puzzle